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<pre><span class="sourceLineNo">001</span>/*<a name="line.1"></a>
<span class="sourceLineNo">002</span> * Copyright (C) 2011 The Guava Authors<a name="line.2"></a>
<span class="sourceLineNo">003</span> *<a name="line.3"></a>
<span class="sourceLineNo">004</span> * Licensed under the Apache License, Version 2.0 (the "License");<a name="line.4"></a>
<span class="sourceLineNo">005</span> * you may not use this file except in compliance with the License.<a name="line.5"></a>
<span class="sourceLineNo">006</span> * You may obtain a copy of the License at<a name="line.6"></a>
<span class="sourceLineNo">007</span> *<a name="line.7"></a>
<span class="sourceLineNo">008</span> * http://www.apache.org/licenses/LICENSE-2.0<a name="line.8"></a>
<span class="sourceLineNo">009</span> *<a name="line.9"></a>
<span class="sourceLineNo">010</span> * Unless required by applicable law or agreed to in writing, software<a name="line.10"></a>
<span class="sourceLineNo">011</span> * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.11"></a>
<span class="sourceLineNo">012</span> * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.12"></a>
<span class="sourceLineNo">013</span> * See the License for the specific language governing permissions and<a name="line.13"></a>
<span class="sourceLineNo">014</span> * limitations under the License.<a name="line.14"></a>
<span class="sourceLineNo">015</span> */<a name="line.15"></a>
<span class="sourceLineNo">016</span><a name="line.16"></a>
<span class="sourceLineNo">017</span>package com.google.common.math;<a name="line.17"></a>
<span class="sourceLineNo">018</span><a name="line.18"></a>
<span class="sourceLineNo">019</span>import static com.google.common.base.Preconditions.checkArgument;<a name="line.19"></a>
<span class="sourceLineNo">020</span>import static com.google.common.math.DoubleUtils.IMPLICIT_BIT;<a name="line.20"></a>
<span class="sourceLineNo">021</span>import static com.google.common.math.DoubleUtils.SIGNIFICAND_BITS;<a name="line.21"></a>
<span class="sourceLineNo">022</span>import static com.google.common.math.DoubleUtils.getSignificand;<a name="line.22"></a>
<span class="sourceLineNo">023</span>import static com.google.common.math.DoubleUtils.isFinite;<a name="line.23"></a>
<span class="sourceLineNo">024</span>import static com.google.common.math.DoubleUtils.isNormal;<a name="line.24"></a>
<span class="sourceLineNo">025</span>import static com.google.common.math.DoubleUtils.scaleNormalize;<a name="line.25"></a>
<span class="sourceLineNo">026</span>import static com.google.common.math.MathPreconditions.checkInRange;<a name="line.26"></a>
<span class="sourceLineNo">027</span>import static com.google.common.math.MathPreconditions.checkNonNegative;<a name="line.27"></a>
<span class="sourceLineNo">028</span>import static com.google.common.math.MathPreconditions.checkRoundingUnnecessary;<a name="line.28"></a>
<span class="sourceLineNo">029</span>import static java.lang.Math.abs;<a name="line.29"></a>
<span class="sourceLineNo">030</span>import static java.lang.Math.copySign;<a name="line.30"></a>
<span class="sourceLineNo">031</span>import static java.lang.Math.getExponent;<a name="line.31"></a>
<span class="sourceLineNo">032</span>import static java.lang.Math.log;<a name="line.32"></a>
<span class="sourceLineNo">033</span>import static java.lang.Math.rint;<a name="line.33"></a>
<span class="sourceLineNo">034</span><a name="line.34"></a>
<span class="sourceLineNo">035</span>import com.google.common.annotations.Beta;<a name="line.35"></a>
<span class="sourceLineNo">036</span>import com.google.common.annotations.VisibleForTesting;<a name="line.36"></a>
<span class="sourceLineNo">037</span>import com.google.common.primitives.Booleans;<a name="line.37"></a>
<span class="sourceLineNo">038</span><a name="line.38"></a>
<span class="sourceLineNo">039</span>import java.math.BigInteger;<a name="line.39"></a>
<span class="sourceLineNo">040</span>import java.math.RoundingMode;<a name="line.40"></a>
<span class="sourceLineNo">041</span><a name="line.41"></a>
<span class="sourceLineNo">042</span>/**<a name="line.42"></a>
<span class="sourceLineNo">043</span> * A class for arithmetic on doubles that is not covered by {@link java.lang.Math}.<a name="line.43"></a>
<span class="sourceLineNo">044</span> *<a name="line.44"></a>
<span class="sourceLineNo">045</span> * @author Louis Wasserman<a name="line.45"></a>
<span class="sourceLineNo">046</span> * @since 11.0<a name="line.46"></a>
<span class="sourceLineNo">047</span> */<a name="line.47"></a>
<span class="sourceLineNo">048</span>@Beta<a name="line.48"></a>
<span class="sourceLineNo">049</span>public final class DoubleMath {<a name="line.49"></a>
<span class="sourceLineNo">050</span>  /*<a name="line.50"></a>
<span class="sourceLineNo">051</span>   * This method returns a value y such that rounding y DOWN (towards zero) gives the same result<a name="line.51"></a>
<span class="sourceLineNo">052</span>   * as rounding x according to the specified mode.<a name="line.52"></a>
<span class="sourceLineNo">053</span>   */<a name="line.53"></a>
<span class="sourceLineNo">054</span>  static double roundIntermediate(double x, RoundingMode mode) {<a name="line.54"></a>
<span class="sourceLineNo">055</span>    if (!isFinite(x)) {<a name="line.55"></a>
<span class="sourceLineNo">056</span>      throw new ArithmeticException("input is infinite or NaN");<a name="line.56"></a>
<span class="sourceLineNo">057</span>    }<a name="line.57"></a>
<span class="sourceLineNo">058</span>    switch (mode) {<a name="line.58"></a>
<span class="sourceLineNo">059</span>      case UNNECESSARY:<a name="line.59"></a>
<span class="sourceLineNo">060</span>        checkRoundingUnnecessary(isMathematicalInteger(x));<a name="line.60"></a>
<span class="sourceLineNo">061</span>        return x;<a name="line.61"></a>
<span class="sourceLineNo">062</span><a name="line.62"></a>
<span class="sourceLineNo">063</span>      case FLOOR:<a name="line.63"></a>
<span class="sourceLineNo">064</span>        if (x &gt;= 0.0 || isMathematicalInteger(x)) {<a name="line.64"></a>
<span class="sourceLineNo">065</span>          return x;<a name="line.65"></a>
<span class="sourceLineNo">066</span>        } else {<a name="line.66"></a>
<span class="sourceLineNo">067</span>          return x - 1.0;<a name="line.67"></a>
<span class="sourceLineNo">068</span>        }<a name="line.68"></a>
<span class="sourceLineNo">069</span><a name="line.69"></a>
<span class="sourceLineNo">070</span>      case CEILING:<a name="line.70"></a>
<span class="sourceLineNo">071</span>        if (x &lt;= 0.0 || isMathematicalInteger(x)) {<a name="line.71"></a>
<span class="sourceLineNo">072</span>          return x;<a name="line.72"></a>
<span class="sourceLineNo">073</span>        } else {<a name="line.73"></a>
<span class="sourceLineNo">074</span>          return x + 1.0;<a name="line.74"></a>
<span class="sourceLineNo">075</span>        }<a name="line.75"></a>
<span class="sourceLineNo">076</span><a name="line.76"></a>
<span class="sourceLineNo">077</span>      case DOWN:<a name="line.77"></a>
<span class="sourceLineNo">078</span>        return x;<a name="line.78"></a>
<span class="sourceLineNo">079</span><a name="line.79"></a>
<span class="sourceLineNo">080</span>      case UP:<a name="line.80"></a>
<span class="sourceLineNo">081</span>        if (isMathematicalInteger(x)) {<a name="line.81"></a>
<span class="sourceLineNo">082</span>          return x;<a name="line.82"></a>
<span class="sourceLineNo">083</span>        } else {<a name="line.83"></a>
<span class="sourceLineNo">084</span>          return x + Math.copySign(1.0, x);<a name="line.84"></a>
<span class="sourceLineNo">085</span>        }<a name="line.85"></a>
<span class="sourceLineNo">086</span><a name="line.86"></a>
<span class="sourceLineNo">087</span>      case HALF_EVEN:<a name="line.87"></a>
<span class="sourceLineNo">088</span>        return rint(x);<a name="line.88"></a>
<span class="sourceLineNo">089</span><a name="line.89"></a>
<span class="sourceLineNo">090</span>      case HALF_UP: {<a name="line.90"></a>
<span class="sourceLineNo">091</span>        double z = rint(x);<a name="line.91"></a>
<span class="sourceLineNo">092</span>        if (abs(x - z) == 0.5) {<a name="line.92"></a>
<span class="sourceLineNo">093</span>          return x + copySign(0.5, x);<a name="line.93"></a>
<span class="sourceLineNo">094</span>        } else {<a name="line.94"></a>
<span class="sourceLineNo">095</span>          return z;<a name="line.95"></a>
<span class="sourceLineNo">096</span>        }<a name="line.96"></a>
<span class="sourceLineNo">097</span>      }<a name="line.97"></a>
<span class="sourceLineNo">098</span><a name="line.98"></a>
<span class="sourceLineNo">099</span>      case HALF_DOWN: {<a name="line.99"></a>
<span class="sourceLineNo">100</span>        double z = rint(x);<a name="line.100"></a>
<span class="sourceLineNo">101</span>        if (abs(x - z) == 0.5) {<a name="line.101"></a>
<span class="sourceLineNo">102</span>          return x;<a name="line.102"></a>
<span class="sourceLineNo">103</span>        } else {<a name="line.103"></a>
<span class="sourceLineNo">104</span>          return z;<a name="line.104"></a>
<span class="sourceLineNo">105</span>        }<a name="line.105"></a>
<span class="sourceLineNo">106</span>      }<a name="line.106"></a>
<span class="sourceLineNo">107</span><a name="line.107"></a>
<span class="sourceLineNo">108</span>      default:<a name="line.108"></a>
<span class="sourceLineNo">109</span>        throw new AssertionError();<a name="line.109"></a>
<span class="sourceLineNo">110</span>    }<a name="line.110"></a>
<span class="sourceLineNo">111</span>  }<a name="line.111"></a>
<span class="sourceLineNo">112</span><a name="line.112"></a>
<span class="sourceLineNo">113</span>  /**<a name="line.113"></a>
<span class="sourceLineNo">114</span>   * Returns the {@code int} value that is equal to {@code x} rounded with the specified rounding<a name="line.114"></a>
<span class="sourceLineNo">115</span>   * mode, if possible.<a name="line.115"></a>
<span class="sourceLineNo">116</span>   *<a name="line.116"></a>
<span class="sourceLineNo">117</span>   * @throws ArithmeticException if<a name="line.117"></a>
<span class="sourceLineNo">118</span>   *         &lt;ul&gt;<a name="line.118"></a>
<span class="sourceLineNo">119</span>   *         &lt;li&gt;{@code x} is infinite or NaN<a name="line.119"></a>
<span class="sourceLineNo">120</span>   *         &lt;li&gt;{@code x}, after being rounded to a mathematical integer using the specified<a name="line.120"></a>
<span class="sourceLineNo">121</span>   *         rounding mode, is either less than {@code Integer.MIN_VALUE} or greater than {@code<a name="line.121"></a>
<span class="sourceLineNo">122</span>   *         Integer.MAX_VALUE}<a name="line.122"></a>
<span class="sourceLineNo">123</span>   *         &lt;li&gt;{@code x} is not a mathematical integer and {@code mode} is<a name="line.123"></a>
<span class="sourceLineNo">124</span>   *         {@link RoundingMode#UNNECESSARY}<a name="line.124"></a>
<span class="sourceLineNo">125</span>   *         &lt;/ul&gt;<a name="line.125"></a>
<span class="sourceLineNo">126</span>   */<a name="line.126"></a>
<span class="sourceLineNo">127</span>  public static int roundToInt(double x, RoundingMode mode) {<a name="line.127"></a>
<span class="sourceLineNo">128</span>    double z = roundIntermediate(x, mode);<a name="line.128"></a>
<span class="sourceLineNo">129</span>    checkInRange(z &gt; MIN_INT_AS_DOUBLE - 1.0 &amp; z &lt; MAX_INT_AS_DOUBLE + 1.0);<a name="line.129"></a>
<span class="sourceLineNo">130</span>    return (int) z;<a name="line.130"></a>
<span class="sourceLineNo">131</span>  }<a name="line.131"></a>
<span class="sourceLineNo">132</span><a name="line.132"></a>
<span class="sourceLineNo">133</span>  private static final double MIN_INT_AS_DOUBLE = -0x1p31;<a name="line.133"></a>
<span class="sourceLineNo">134</span>  private static final double MAX_INT_AS_DOUBLE = 0x1p31 - 1.0;<a name="line.134"></a>
<span class="sourceLineNo">135</span><a name="line.135"></a>
<span class="sourceLineNo">136</span>  /**<a name="line.136"></a>
<span class="sourceLineNo">137</span>   * Returns the {@code long} value that is equal to {@code x} rounded with the specified rounding<a name="line.137"></a>
<span class="sourceLineNo">138</span>   * mode, if possible.<a name="line.138"></a>
<span class="sourceLineNo">139</span>   *<a name="line.139"></a>
<span class="sourceLineNo">140</span>   * @throws ArithmeticException if<a name="line.140"></a>
<span class="sourceLineNo">141</span>   *         &lt;ul&gt;<a name="line.141"></a>
<span class="sourceLineNo">142</span>   *         &lt;li&gt;{@code x} is infinite or NaN<a name="line.142"></a>
<span class="sourceLineNo">143</span>   *         &lt;li&gt;{@code x}, after being rounded to a mathematical integer using the specified<a name="line.143"></a>
<span class="sourceLineNo">144</span>   *         rounding mode, is either less than {@code Long.MIN_VALUE} or greater than {@code<a name="line.144"></a>
<span class="sourceLineNo">145</span>   *         Long.MAX_VALUE}<a name="line.145"></a>
<span class="sourceLineNo">146</span>   *         &lt;li&gt;{@code x} is not a mathematical integer and {@code mode} is<a name="line.146"></a>
<span class="sourceLineNo">147</span>   *         {@link RoundingMode#UNNECESSARY}<a name="line.147"></a>
<span class="sourceLineNo">148</span>   *         &lt;/ul&gt;<a name="line.148"></a>
<span class="sourceLineNo">149</span>   */<a name="line.149"></a>
<span class="sourceLineNo">150</span>  public static long roundToLong(double x, RoundingMode mode) {<a name="line.150"></a>
<span class="sourceLineNo">151</span>    double z = roundIntermediate(x, mode);<a name="line.151"></a>
<span class="sourceLineNo">152</span>    checkInRange(MIN_LONG_AS_DOUBLE - z &lt; 1.0 &amp; z &lt; MAX_LONG_AS_DOUBLE_PLUS_ONE);<a name="line.152"></a>
<span class="sourceLineNo">153</span>    return (long) z;<a name="line.153"></a>
<span class="sourceLineNo">154</span>  }<a name="line.154"></a>
<span class="sourceLineNo">155</span><a name="line.155"></a>
<span class="sourceLineNo">156</span>  private static final double MIN_LONG_AS_DOUBLE = -0x1p63;<a name="line.156"></a>
<span class="sourceLineNo">157</span>  /*<a name="line.157"></a>
<span class="sourceLineNo">158</span>   * We cannot store Long.MAX_VALUE as a double without losing precision.  Instead, we store<a name="line.158"></a>
<span class="sourceLineNo">159</span>   * Long.MAX_VALUE + 1 == -Long.MIN_VALUE, and then offset all comparisons by 1.<a name="line.159"></a>
<span class="sourceLineNo">160</span>   */<a name="line.160"></a>
<span class="sourceLineNo">161</span>  private static final double MAX_LONG_AS_DOUBLE_PLUS_ONE = 0x1p63;<a name="line.161"></a>
<span class="sourceLineNo">162</span><a name="line.162"></a>
<span class="sourceLineNo">163</span>  /**<a name="line.163"></a>
<span class="sourceLineNo">164</span>   * Returns the {@code BigInteger} value that is equal to {@code x} rounded with the specified<a name="line.164"></a>
<span class="sourceLineNo">165</span>   * rounding mode, if possible.<a name="line.165"></a>
<span class="sourceLineNo">166</span>   *<a name="line.166"></a>
<span class="sourceLineNo">167</span>   * @throws ArithmeticException if<a name="line.167"></a>
<span class="sourceLineNo">168</span>   *         &lt;ul&gt;<a name="line.168"></a>
<span class="sourceLineNo">169</span>   *         &lt;li&gt;{@code x} is infinite or NaN<a name="line.169"></a>
<span class="sourceLineNo">170</span>   *         &lt;li&gt;{@code x} is not a mathematical integer and {@code mode} is<a name="line.170"></a>
<span class="sourceLineNo">171</span>   *         {@link RoundingMode#UNNECESSARY}<a name="line.171"></a>
<span class="sourceLineNo">172</span>   *         &lt;/ul&gt;<a name="line.172"></a>
<span class="sourceLineNo">173</span>   */<a name="line.173"></a>
<span class="sourceLineNo">174</span>  public static BigInteger roundToBigInteger(double x, RoundingMode mode) {<a name="line.174"></a>
<span class="sourceLineNo">175</span>    x = roundIntermediate(x, mode);<a name="line.175"></a>
<span class="sourceLineNo">176</span>    if (MIN_LONG_AS_DOUBLE - x &lt; 1.0 &amp; x &lt; MAX_LONG_AS_DOUBLE_PLUS_ONE) {<a name="line.176"></a>
<span class="sourceLineNo">177</span>      return BigInteger.valueOf((long) x);<a name="line.177"></a>
<span class="sourceLineNo">178</span>    }<a name="line.178"></a>
<span class="sourceLineNo">179</span>    int exponent = getExponent(x);<a name="line.179"></a>
<span class="sourceLineNo">180</span>    long significand = getSignificand(x);<a name="line.180"></a>
<span class="sourceLineNo">181</span>    BigInteger result = BigInteger.valueOf(significand).shiftLeft(exponent - SIGNIFICAND_BITS);<a name="line.181"></a>
<span class="sourceLineNo">182</span>    return (x &lt; 0) ? result.negate() : result;<a name="line.182"></a>
<span class="sourceLineNo">183</span>  }<a name="line.183"></a>
<span class="sourceLineNo">184</span><a name="line.184"></a>
<span class="sourceLineNo">185</span>  /**<a name="line.185"></a>
<span class="sourceLineNo">186</span>   * Returns {@code true} if {@code x} is exactly equal to {@code 2^k} for some finite integer<a name="line.186"></a>
<span class="sourceLineNo">187</span>   * {@code k}.<a name="line.187"></a>
<span class="sourceLineNo">188</span>   */<a name="line.188"></a>
<span class="sourceLineNo">189</span>  public static boolean isPowerOfTwo(double x) {<a name="line.189"></a>
<span class="sourceLineNo">190</span>    return x &gt; 0.0 &amp;&amp; isFinite(x) &amp;&amp; LongMath.isPowerOfTwo(getSignificand(x));<a name="line.190"></a>
<span class="sourceLineNo">191</span>  }<a name="line.191"></a>
<span class="sourceLineNo">192</span><a name="line.192"></a>
<span class="sourceLineNo">193</span>  /**<a name="line.193"></a>
<span class="sourceLineNo">194</span>   * Returns the base 2 logarithm of a double value.<a name="line.194"></a>
<span class="sourceLineNo">195</span>   *<a name="line.195"></a>
<span class="sourceLineNo">196</span>   * &lt;p&gt;Special cases:<a name="line.196"></a>
<span class="sourceLineNo">197</span>   * &lt;ul&gt;<a name="line.197"></a>
<span class="sourceLineNo">198</span>   * &lt;li&gt;If {@code x} is NaN or less than zero, the result is NaN.<a name="line.198"></a>
<span class="sourceLineNo">199</span>   * &lt;li&gt;If {@code x} is positive infinity, the result is positive infinity.<a name="line.199"></a>
<span class="sourceLineNo">200</span>   * &lt;li&gt;If {@code x} is positive or negative zero, the result is negative infinity.<a name="line.200"></a>
<span class="sourceLineNo">201</span>   * &lt;/ul&gt;<a name="line.201"></a>
<span class="sourceLineNo">202</span>   *<a name="line.202"></a>
<span class="sourceLineNo">203</span>   * &lt;p&gt;The computed result is within 1 ulp of the exact result.<a name="line.203"></a>
<span class="sourceLineNo">204</span>   *<a name="line.204"></a>
<span class="sourceLineNo">205</span>   * &lt;p&gt;If the result of this method will be immediately rounded to an {@code int},<a name="line.205"></a>
<span class="sourceLineNo">206</span>   * {@link #log2(double, RoundingMode)} is faster.<a name="line.206"></a>
<span class="sourceLineNo">207</span>   */<a name="line.207"></a>
<span class="sourceLineNo">208</span>  public static double log2(double x) {<a name="line.208"></a>
<span class="sourceLineNo">209</span>    return log(x) / LN_2; // surprisingly within 1 ulp according to tests<a name="line.209"></a>
<span class="sourceLineNo">210</span>  }<a name="line.210"></a>
<span class="sourceLineNo">211</span><a name="line.211"></a>
<span class="sourceLineNo">212</span>  private static final double LN_2 = log(2);<a name="line.212"></a>
<span class="sourceLineNo">213</span><a name="line.213"></a>
<span class="sourceLineNo">214</span>  /**<a name="line.214"></a>
<span class="sourceLineNo">215</span>   * Returns the base 2 logarithm of a double value, rounded with the specified rounding mode to an<a name="line.215"></a>
<span class="sourceLineNo">216</span>   * {@code int}.<a name="line.216"></a>
<span class="sourceLineNo">217</span>   *<a name="line.217"></a>
<span class="sourceLineNo">218</span>   * &lt;p&gt;Regardless of the rounding mode, this is faster than {@code (int) log2(x)}.<a name="line.218"></a>
<span class="sourceLineNo">219</span>   *<a name="line.219"></a>
<span class="sourceLineNo">220</span>   * @throws IllegalArgumentException if {@code x &lt;= 0.0}, {@code x} is NaN, or {@code x} is<a name="line.220"></a>
<span class="sourceLineNo">221</span>   *         infinite<a name="line.221"></a>
<span class="sourceLineNo">222</span>   */<a name="line.222"></a>
<span class="sourceLineNo">223</span>  @SuppressWarnings("fallthrough")<a name="line.223"></a>
<span class="sourceLineNo">224</span>  public static int log2(double x, RoundingMode mode) {<a name="line.224"></a>
<span class="sourceLineNo">225</span>    checkArgument(x &gt; 0.0 &amp;&amp; isFinite(x), "x must be positive and finite");<a name="line.225"></a>
<span class="sourceLineNo">226</span>    int exponent = getExponent(x);<a name="line.226"></a>
<span class="sourceLineNo">227</span>    if (!isNormal(x)) {<a name="line.227"></a>
<span class="sourceLineNo">228</span>      return log2(x * IMPLICIT_BIT, mode) - SIGNIFICAND_BITS;<a name="line.228"></a>
<span class="sourceLineNo">229</span>      // Do the calculation on a normal value.<a name="line.229"></a>
<span class="sourceLineNo">230</span>    }<a name="line.230"></a>
<span class="sourceLineNo">231</span>    // x is positive, finite, and normal<a name="line.231"></a>
<span class="sourceLineNo">232</span>    boolean increment;<a name="line.232"></a>
<span class="sourceLineNo">233</span>    switch (mode) {<a name="line.233"></a>
<span class="sourceLineNo">234</span>      case UNNECESSARY:<a name="line.234"></a>
<span class="sourceLineNo">235</span>        checkRoundingUnnecessary(isPowerOfTwo(x));<a name="line.235"></a>
<span class="sourceLineNo">236</span>        // fall through<a name="line.236"></a>
<span class="sourceLineNo">237</span>      case FLOOR:<a name="line.237"></a>
<span class="sourceLineNo">238</span>        increment = false;<a name="line.238"></a>
<span class="sourceLineNo">239</span>        break;<a name="line.239"></a>
<span class="sourceLineNo">240</span>      case CEILING:<a name="line.240"></a>
<span class="sourceLineNo">241</span>        increment = !isPowerOfTwo(x);<a name="line.241"></a>
<span class="sourceLineNo">242</span>        break;<a name="line.242"></a>
<span class="sourceLineNo">243</span>      case DOWN:<a name="line.243"></a>
<span class="sourceLineNo">244</span>        increment = exponent &lt; 0 &amp; !isPowerOfTwo(x);<a name="line.244"></a>
<span class="sourceLineNo">245</span>        break;<a name="line.245"></a>
<span class="sourceLineNo">246</span>      case UP:<a name="line.246"></a>
<span class="sourceLineNo">247</span>        increment = exponent &gt;= 0 &amp; !isPowerOfTwo(x);<a name="line.247"></a>
<span class="sourceLineNo">248</span>        break;<a name="line.248"></a>
<span class="sourceLineNo">249</span>      case HALF_DOWN:<a name="line.249"></a>
<span class="sourceLineNo">250</span>      case HALF_EVEN:<a name="line.250"></a>
<span class="sourceLineNo">251</span>      case HALF_UP:<a name="line.251"></a>
<span class="sourceLineNo">252</span>        double xScaled = scaleNormalize(x);<a name="line.252"></a>
<span class="sourceLineNo">253</span>        // sqrt(2) is irrational, and the spec is relative to the "exact numerical result,"<a name="line.253"></a>
<span class="sourceLineNo">254</span>        // so log2(x) is never exactly exponent + 0.5.<a name="line.254"></a>
<span class="sourceLineNo">255</span>        increment = (xScaled * xScaled) &gt; 2.0;<a name="line.255"></a>
<span class="sourceLineNo">256</span>        break;<a name="line.256"></a>
<span class="sourceLineNo">257</span>      default:<a name="line.257"></a>
<span class="sourceLineNo">258</span>        throw new AssertionError();<a name="line.258"></a>
<span class="sourceLineNo">259</span>    }<a name="line.259"></a>
<span class="sourceLineNo">260</span>    return increment ? exponent + 1 : exponent;<a name="line.260"></a>
<span class="sourceLineNo">261</span>  }<a name="line.261"></a>
<span class="sourceLineNo">262</span><a name="line.262"></a>
<span class="sourceLineNo">263</span>  /**<a name="line.263"></a>
<span class="sourceLineNo">264</span>   * Returns {@code true} if {@code x} represents a mathematical integer.<a name="line.264"></a>
<span class="sourceLineNo">265</span>   *<a name="line.265"></a>
<span class="sourceLineNo">266</span>   * &lt;p&gt;This is equivalent to, but not necessarily implemented as, the expression {@code<a name="line.266"></a>
<span class="sourceLineNo">267</span>   * !Double.isNaN(x) &amp;&amp; !Double.isInfinite(x) &amp;&amp; x == Math.rint(x)}.<a name="line.267"></a>
<span class="sourceLineNo">268</span>   */<a name="line.268"></a>
<span class="sourceLineNo">269</span>  public static boolean isMathematicalInteger(double x) {<a name="line.269"></a>
<span class="sourceLineNo">270</span>    return isFinite(x)<a name="line.270"></a>
<span class="sourceLineNo">271</span>        &amp;&amp; (x == 0.0 ||<a name="line.271"></a>
<span class="sourceLineNo">272</span>            SIGNIFICAND_BITS - Long.numberOfTrailingZeros(getSignificand(x)) &lt;= getExponent(x));<a name="line.272"></a>
<span class="sourceLineNo">273</span>  }<a name="line.273"></a>
<span class="sourceLineNo">274</span><a name="line.274"></a>
<span class="sourceLineNo">275</span>  /**<a name="line.275"></a>
<span class="sourceLineNo">276</span>   * Returns {@code n!}, that is, the product of the first {@code n} positive<a name="line.276"></a>
<span class="sourceLineNo">277</span>   * integers, {@code 1} if {@code n == 0}, or e n!}, or<a name="line.277"></a>
<span class="sourceLineNo">278</span>   * {@link Double#POSITIVE_INFINITY} if {@code n! &gt; Double.MAX_VALUE}.<a name="line.278"></a>
<span class="sourceLineNo">279</span>   *<a name="line.279"></a>
<span class="sourceLineNo">280</span>   * &lt;p&gt;The result is within 1 ulp of the true value.<a name="line.280"></a>
<span class="sourceLineNo">281</span>   *<a name="line.281"></a>
<span class="sourceLineNo">282</span>   * @throws IllegalArgumentException if {@code n &lt; 0}<a name="line.282"></a>
<span class="sourceLineNo">283</span>   */<a name="line.283"></a>
<span class="sourceLineNo">284</span>  public static double factorial(int n) {<a name="line.284"></a>
<span class="sourceLineNo">285</span>    checkNonNegative("n", n);<a name="line.285"></a>
<span class="sourceLineNo">286</span>    if (n &gt; MAX_FACTORIAL) {<a name="line.286"></a>
<span class="sourceLineNo">287</span>      return Double.POSITIVE_INFINITY;<a name="line.287"></a>
<span class="sourceLineNo">288</span>    } else {<a name="line.288"></a>
<span class="sourceLineNo">289</span>      // Multiplying the last (n &amp; 0xf) values into their own accumulator gives a more accurate<a name="line.289"></a>
<span class="sourceLineNo">290</span>      // result than multiplying by EVERY_SIXTEENTH_FACTORIAL[n &gt;&gt; 4] directly.<a name="line.290"></a>
<span class="sourceLineNo">291</span>      double accum = 1.0;<a name="line.291"></a>
<span class="sourceLineNo">292</span>      for (int i = 1 + (n &amp; ~0xf); i &lt;= n; i++) {<a name="line.292"></a>
<span class="sourceLineNo">293</span>        accum *= i;<a name="line.293"></a>
<span class="sourceLineNo">294</span>      }<a name="line.294"></a>
<span class="sourceLineNo">295</span>      return accum * EVERY_SIXTEENTH_FACTORIAL[n &gt;&gt; 4];<a name="line.295"></a>
<span class="sourceLineNo">296</span>    }<a name="line.296"></a>
<span class="sourceLineNo">297</span>  }<a name="line.297"></a>
<span class="sourceLineNo">298</span><a name="line.298"></a>
<span class="sourceLineNo">299</span>  @VisibleForTesting<a name="line.299"></a>
<span class="sourceLineNo">300</span>  static final int MAX_FACTORIAL = 170;<a name="line.300"></a>
<span class="sourceLineNo">301</span><a name="line.301"></a>
<span class="sourceLineNo">302</span>  @VisibleForTesting<a name="line.302"></a>
<span class="sourceLineNo">303</span>  static final double[] EVERY_SIXTEENTH_FACTORIAL = {<a name="line.303"></a>
<span class="sourceLineNo">304</span>      0x1.0p0,<a name="line.304"></a>
<span class="sourceLineNo">305</span>      0x1.30777758p44,<a name="line.305"></a>
<span class="sourceLineNo">306</span>      0x1.956ad0aae33a4p117,<a name="line.306"></a>
<span class="sourceLineNo">307</span>      0x1.ee69a78d72cb6p202,<a name="line.307"></a>
<span class="sourceLineNo">308</span>      0x1.fe478ee34844ap295,<a name="line.308"></a>
<span class="sourceLineNo">309</span>      0x1.c619094edabffp394,<a name="line.309"></a>
<span class="sourceLineNo">310</span>      0x1.3638dd7bd6347p498,<a name="line.310"></a>
<span class="sourceLineNo">311</span>      0x1.7cac197cfe503p605,<a name="line.311"></a>
<span class="sourceLineNo">312</span>      0x1.1e5dfc140e1e5p716,<a name="line.312"></a>
<span class="sourceLineNo">313</span>      0x1.8ce85fadb707ep829,<a name="line.313"></a>
<span class="sourceLineNo">314</span>      0x1.95d5f3d928edep945};<a name="line.314"></a>
<span class="sourceLineNo">315</span><a name="line.315"></a>
<span class="sourceLineNo">316</span>  /**<a name="line.316"></a>
<span class="sourceLineNo">317</span>   * Returns {@code true} if {@code a} and {@code b} are within {@code tolerance} of each other.<a name="line.317"></a>
<span class="sourceLineNo">318</span>   *<a name="line.318"></a>
<span class="sourceLineNo">319</span>   * &lt;p&gt;Technically speaking, this is equivalent to<a name="line.319"></a>
<span class="sourceLineNo">320</span>   * {@code Math.abs(a - b) &lt;= tolerance || Double.valueOf(a).equals(Double.valueOf(b))}.<a name="line.320"></a>
<span class="sourceLineNo">321</span>   *<a name="line.321"></a>
<span class="sourceLineNo">322</span>   * &lt;p&gt;Notable special cases include:<a name="line.322"></a>
<span class="sourceLineNo">323</span>   * &lt;ul&gt;<a name="line.323"></a>
<span class="sourceLineNo">324</span>   * &lt;li&gt;All NaNs are fuzzily equal.<a name="line.324"></a>
<span class="sourceLineNo">325</span>   * &lt;li&gt;If {@code a == b}, then {@code a} and {@code b} are always fuzzily equal.<a name="line.325"></a>
<span class="sourceLineNo">326</span>   * &lt;li&gt;Positive and negative zero are always fuzzily equal.<a name="line.326"></a>
<span class="sourceLineNo">327</span>   * &lt;li&gt;If {@code tolerance} is zero, and neither {@code a} nor {@code b} is NaN, then<a name="line.327"></a>
<span class="sourceLineNo">328</span>   * {@code a} and {@code b} are fuzzily equal if and only if {@code a == b}.<a name="line.328"></a>
<span class="sourceLineNo">329</span>   * &lt;li&gt;With {@link Double#POSITIVE_INFINITY} tolerance, all non-NaN values are fuzzily equal.<a name="line.329"></a>
<span class="sourceLineNo">330</span>   * &lt;li&gt;With finite tolerance, {@code Double.POSITIVE_INFINITY} and {@code<a name="line.330"></a>
<span class="sourceLineNo">331</span>   * Double.NEGATIVE_INFINITY} are fuzzily equal only to themselves.<a name="line.331"></a>
<span class="sourceLineNo">332</span>   * &lt;/li&gt;<a name="line.332"></a>
<span class="sourceLineNo">333</span>   *<a name="line.333"></a>
<span class="sourceLineNo">334</span>   * &lt;p&gt;This is reflexive and symmetric, but &lt;em&gt;not&lt;/em&gt; transitive, so it is &lt;em&gt;not&lt;/em&gt; an<a name="line.334"></a>
<span class="sourceLineNo">335</span>   * equivalence relation and &lt;em&gt;not&lt;/em&gt; suitable for use in {@link Object#equals}<a name="line.335"></a>
<span class="sourceLineNo">336</span>   * implementations.<a name="line.336"></a>
<span class="sourceLineNo">337</span>   *<a name="line.337"></a>
<span class="sourceLineNo">338</span>   * @throws IllegalArgumentException if {@code tolerance} is {@code &lt; 0} or NaN<a name="line.338"></a>
<span class="sourceLineNo">339</span>   * @since 13.0<a name="line.339"></a>
<span class="sourceLineNo">340</span>   */<a name="line.340"></a>
<span class="sourceLineNo">341</span>  @Beta<a name="line.341"></a>
<span class="sourceLineNo">342</span>  public static boolean fuzzyEquals(double a, double b, double tolerance) {<a name="line.342"></a>
<span class="sourceLineNo">343</span>    MathPreconditions.checkNonNegative("tolerance", tolerance);<a name="line.343"></a>
<span class="sourceLineNo">344</span>    return<a name="line.344"></a>
<span class="sourceLineNo">345</span>          Math.copySign(a - b, 1.0) &lt;= tolerance<a name="line.345"></a>
<span class="sourceLineNo">346</span>           // copySign(x, 1.0) is a branch-free version of abs(x), but with different NaN semantics<a name="line.346"></a>
<span class="sourceLineNo">347</span>          || (a == b) // needed to ensure that infinities equal themselves<a name="line.347"></a>
<span class="sourceLineNo">348</span>          || ((a != a) &amp;&amp; (b != b)); // x != x is equivalent to Double.isNaN(x), but faster<a name="line.348"></a>
<span class="sourceLineNo">349</span>  }<a name="line.349"></a>
<span class="sourceLineNo">350</span><a name="line.350"></a>
<span class="sourceLineNo">351</span>  /**<a name="line.351"></a>
<span class="sourceLineNo">352</span>   * Compares {@code a} and {@code b} "fuzzily," with a tolerance for nearly-equal values.<a name="line.352"></a>
<span class="sourceLineNo">353</span>   *<a name="line.353"></a>
<span class="sourceLineNo">354</span>   * &lt;p&gt;This method is equivalent to<a name="line.354"></a>
<span class="sourceLineNo">355</span>   * {@code fuzzyEquals(a, b, tolerance) ? 0 : Double.compare(a, b)}. In particular, like<a name="line.355"></a>
<span class="sourceLineNo">356</span>   * {@link Double#compare(double, double)}, it treats all NaN values as equal and greater than all<a name="line.356"></a>
<span class="sourceLineNo">357</span>   * other values (including {@link Double#POSITIVE_INFINITY}).<a name="line.357"></a>
<span class="sourceLineNo">358</span>   *<a name="line.358"></a>
<span class="sourceLineNo">359</span>   * &lt;p&gt;This is &lt;em&gt;not&lt;/em&gt; a total ordering and is &lt;em&gt;not&lt;/em&gt; suitable for use in<a name="line.359"></a>
<span class="sourceLineNo">360</span>   * {@link Comparable#compareTo} implementations.  In particular, it is not transitive.<a name="line.360"></a>
<span class="sourceLineNo">361</span>   *<a name="line.361"></a>
<span class="sourceLineNo">362</span>   * @throws IllegalArgumentException if {@code tolerance} is {@code &lt; 0} or NaN<a name="line.362"></a>
<span class="sourceLineNo">363</span>   * @since 13.0<a name="line.363"></a>
<span class="sourceLineNo">364</span>   */<a name="line.364"></a>
<span class="sourceLineNo">365</span>  @Beta<a name="line.365"></a>
<span class="sourceLineNo">366</span>  public static int fuzzyCompare(double a, double b, double tolerance) {<a name="line.366"></a>
<span class="sourceLineNo">367</span>    if (fuzzyEquals(a, b, tolerance)) {<a name="line.367"></a>
<span class="sourceLineNo">368</span>      return 0;<a name="line.368"></a>
<span class="sourceLineNo">369</span>    } else if (a &lt; b) {<a name="line.369"></a>
<span class="sourceLineNo">370</span>      return -1;<a name="line.370"></a>
<span class="sourceLineNo">371</span>    } else if (a &gt; b) {<a name="line.371"></a>
<span class="sourceLineNo">372</span>      return 1;<a name="line.372"></a>
<span class="sourceLineNo">373</span>    } else {<a name="line.373"></a>
<span class="sourceLineNo">374</span>      return Booleans.compare(Double.isNaN(a), Double.isNaN(b));<a name="line.374"></a>
<span class="sourceLineNo">375</span>    }<a name="line.375"></a>
<span class="sourceLineNo">376</span>  }<a name="line.376"></a>
<span class="sourceLineNo">377</span><a name="line.377"></a>
<span class="sourceLineNo">378</span>  private DoubleMath() {}<a name="line.378"></a>
<span class="sourceLineNo">379</span>}<a name="line.379"></a>




























































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